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Analysis of a Pressure-Robust Hybridized Discontinuous Galerkin Method for the Stationary Navier–Stokes Equations

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Abstract

We present well-posedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the Navier–Stokes problem proposed in Rhebergen and Wells (J Sci Comput 76(3):1484–1501, 2018. https://doi.org/10.1007/s10915-018-0671-4). This scheme was shown to result in an approximate velocity field that is pointwise divergence-free and divergence-conforming. As a consequence we show that the velocity error estimate is independent of the pressure. Furthermore, we show that estimates for both the velocity and pressure are optimal. Numerical examples demonstrate pressure-robustness and optimality of the scheme.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, Waterloo, N2L 3G1, Canada

    Keegan L. A. Kirk & Sander Rhebergen

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  1. Keegan L. A. Kirk
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  2. Sander Rhebergen
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Correspondence to Keegan L. A. Kirk.

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SR gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada through the Discovery Grant Program (RGPIN-05606-2015) and the Discovery Accelerator Supplement (RGPAS-478018-2015).

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Kirk, K.L.A., Rhebergen, S. Analysis of a Pressure-Robust Hybridized Discontinuous Galerkin Method for the Stationary Navier–Stokes Equations. J Sci Comput 81, 881–897 (2019). https://doi.org/10.1007/s10915-019-01040-y

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